Financial markets, betting markets and general prediction markets are cases of a centrally organized market where the participants submit bids for contingent claims over the outcome of a future event and the market organizer must determine which bids to accept. In these markets, a bidder selects a set of future states and a price at which he is willing to buy the contingent claims on those states. By accepting a bid on those claims, the market organizer agrees to pay the bidder a fixed amount if one of the bidder's selected states is realized. These markets may be run as call auctions where the organizer holds the auction open until a certain time and then determines the bids to accept and reject.
Centralized organization of a market is useful in instances where the number of traders interested in trading claims over some event is small and there is not a small set of claim formats that everyone is interested in trading. By central organization, we mean that all traders will interact with one market organizer who will conduct trades. The market organizer will issue and guarantee all claims for the market. Without central organization, reasonable liquidity may be difficult to achieve since the cost of making transactions may be high as individual traders may need to conduct several trades to create the specific claim payouts that they desire.
In a centrally organized market, we can think of the traders as making orders to the market organizer. To actually run this type of market, a mechanism is needed to inform the market organizer of which orders to accept and which orders to reject. Many mechanisms are possible, having many different features. When considering potential mechanisms, there are several features that are often desirable. First, it is often valuable to allow market traders to place limit orders. Most actual financial trading includes limit orders where traders express a limit on the price they are willing to pay and/or a limit on the number of shares that they desire. This makes trading more efficient by reducing the number of interactions that the market organizer has with the traders. Secondly, a mechanism typically includes an objective for the market organizer to optimize, e.g., to accept the largest number of orders or to accept the greatest dollar value of orders.
From the individual trader or market participant's point of view, it is often valuable for the market organizer to announce market prices at the time of accepting and rejecting orders. An order's calculated market price is simply the sum of the prices of the individual states that are specified in the order. It is also valuable to the participant if the market organizer agrees to fully accept any order with a limit price greater than or equal to the calculated market price of the order while rejecting any order with a lower limit price. We will refer to this requirement as the price consistency requirement.
There are many available mechanisms to solve this problem. However, only so-called parimutuel mechanisms possess the key characteristic that they are self-funding. In a parimutuel mechanism, the market organizer has no risk of suffering a loss regardless of the outcome of the event in question. A parimutuel mechanism is defined as a mechanism where all the promised payouts to traders are funded exclusively by the accepted orders. The most prevalent use of parimutuel mechanisms is in horse racing betting.
In a traditional parimutuel approach, the market organizer would charge the market participants a fixed amount of money to make an order containing a claim over one particular state. All orders would be accepted. When the market organizer closes the market and one of the states is realized, the total money collected will be divided out to the holders of claims on that state in proportion of the number of orders that they hold (the market organizer could take out his commission before this distribution). This mechanism exposes the market organizer to no risk and has the advantage of accepting all orders. However, one major drawback is that the actual payout to a participant with an order for the realized state will be unknown at the time the participant is placing the order. When the participant's order is accepted, the market organizer could tell her what the payout would be if there were no more orders in the market. However, subsequent orders will change the payouts for realized states. This result does not fit well with the desire of market participants to hold contingent claim securities with known state-dependent payouts.
A limit order parimutuel approach, on the other hand, will pay a predetermined amount to each holder of a bid containing a claim on the realized state, and it allows participants to submit price and quantity limits for their orders. Lange and Economides, in “A parimutuel market microstructure for contingent claims,” European Financial Management, 11(1):25-49, 2005, have provided a parimutuel market model (PMM) for a contingent claims market that is run by a call auction. The market organizer will receive orders for a period of time until the market is closed. Their mechanism will then determine a market price (or implied price) for an order on each state and determine which orders to accept. The distinction between this mechanism and the traditional parimutuel is that the market organizer guarantees a fixed payout if an order is accepted and one of its specified states is realized. Each market participant will specify a limit price corresponding to the maximum amount she is willing to pay for a contingent claim order. The market organizer will then determine whether to accept their orders and what price to charge.
Despite its many positive characteristics, the Lange and Economides model does not have an efficient computational solution. Specifically, because some of the required constraints of their model are not convex, their model requires special techniques to find the global optimum, and there is no guarantee that those techniques will yield a solution in polynomial time.
On another front, Yang and Ng have recently developed an alternative limit order parimutuel model in their 2003 paper “Qualified-Bound-Pricing methods for combinatorial contract auctions.” They have created a linear parimutuel model with a different objective function and a two-stage solution procedure. Their mechanism has many of the same positive characteristics as the Lange and Economides model such as being self-funding, satisfying the price consistency requirement, and providing a guaranteed payout to accepted orders which include the realized state. However, one drawback with this approach is that the solution procedure is iterative and may require one to solve a linear program many times to determine the solution. Another, and perhaps more serious issue is that this model can produce an optimal solution which contains negative state prices.